Curve-drawing apparatus

ABSTRACT

Drawing apparatus useful for tracing parabolic type curves on a coordinate system. The apparatus includes a flexible resilient member having one end fixedly attached to a support pedestal such that the apparatus can be positioned with one end of the elastic member tangent to a base line in the coordinate system. A second end of the elastic member is pivotally connected to a support arm so that the elastic member can be moved in a controlled manner to produce a family of parabolic type curves. The support arm is pivotally and slideably connected to the support pedestal and has one end mounted for movement along a pre-selected guide element which positions the elastic member in numerous positions for drawing a plurality of parabolic type curves. In an alternative embodiment, an arcuate support arm in combination with a locking mechanism is utilized to maintain the elastic member in a preselected position for tracing the parabolic type curve.

United States Patent 1191 Harris Dec. 23, 1975 CURVE-DRAWING APPARATUS Timothy L. Harris, 1304 Bidwell, West St. Paul, Minn. 55118 221 Filed: Mar. 27, 1975 211 Appl. No. 562,479

[76] Inventor:

[52] US. Cl 33/177; 33/27 R; 33/27 H 51 int. c1. B43L 13/22 [58] Field of Search 33/27 H, 27 K, 27 R, 30 B, 33/30 C, 30 E, 176, 177

[56] References Cited UNITED STATES PATENTS 1,091,246 3/1914 Roehrig 33/177 1,690,540 11/1928 Klein 33/177 1,953,282 4/1934 Weston... 33/177 2,001,949 5/1935 Weston 33/177 3,388,475 6/1968 Yoshioka 33/177 3,624,912 12/1971 Voss et al. 33/27 H Primary EtaminerRichard E. Aegerter Assistant Examiner-Charles E. Phillips [5 7] ABSTRACT Drawing apparatus useful for tracing parabolic type curves on a coordinate system. The apparatus includes a flexible resilient member having one end fixedly attached to a support pedestal such that the apparatus can be positioned with one end of the elastic member tangent to a base line in the coordinate system. A second end of the elastic member is pivotally connected to a support arm so that the elastic member can be moved in a controlled manner to produce a family of parabolic type curves. The support arm is pivotally and slideably connected to the support pedestal and has one end mounted for movement along a preselected guide element which positions the elastic member in numerous positions for drawing a plurality of parabolic type curves. In an alternative embodiment, an arcuate support arm in combination with a locking mechanism is utilized to maintain the elastic member in a pre-selected position for tracing the parabolic type curve.

6 Claims, 10 Drawing Figures U.S; Patent Dec. 23, 1975 Sheet 1 of 3 3,927,477

FlG. 2

us. Patent Dec.23,1975 sheath 3,927,477

D 7D2f03 DIRECTRIX SPECIFIED CURVE GUIDE CURVE FIG IO CURVE-DRAWING APPARATUS BACKGROUND OF THE INVENTION Various instruments have long been used for drawing :urved lines. Certain of these devices have been utilized for drawing particular curves such as parabolic curves. Since parabolas are frequently utilized by draftsman in the presentation of various scientific and technical data, there is a particular need for drawing devices which allow a parabolic type curve to be traced onto a coordinate system.

A parabola is generally defined as the locus of points which are equidistant from a given point (i.e. the focus I of the parabola) and a given straight line (i.e. the directrix of the parabola). If the parabola is drawn with its center on a vertical Y-axis and the directrix is parallel to a X-axis, the point on the Y-axis which bisects the parabola is known as the vertex of the parabola and the parabola is tangent to an imaginary line through the vertex which is parallel to the directrix. The equation for a parabola is: y=(K/4y,)X where K is a constant and y is the coordinate for the focus. A family of parabolas would have the same basic equation with different values for the constant K and each parabola would have the same vertex.

Because of these various properties of parabolic geometry and because of the frequent need for drawing parabolic type curves, various devices have been marketed which allow a parabolic type curve to be traced along a drafting element. See for example the patents of Poslusney, US. Pat. No. 3,311,981; Pureka, US. Pat. No. 2,557,999; and Hoglund, US. Pat. No. 3,186,268. In such devices a relatively complex apparatus is utilized for drawing parabolic type curves. Because of this relative complexity such devices are frequently utilized as permanent installations in adrafting department or on a drafting table, This may restrict the versatility of use of the instruments. In addition, such devices may require a relatively high degree of skill to use and are relatively expensive to manufacture and maintain, compared to simpler drafting instruments.

SUMMARY The present invention is a relatively simple device useful in drawing exponential curves, particularly parabolic type curves. An elastic resilient member is utilized as a guide for tracing the exponential curve. One end of the elastic member is securely anchored to a support pedestal which positions it adjacent a coordinate system with the fixed end of the elastic member tangent to a base line in the coordinate system. The second end of the elastic member is free to move in a guided path dictated by the movement of a support arm. In one preferred embodiment, the support arm is pivotally and slideably attached to the support pedestal. One end of the support arm is pivotally attached to the movable end of the elastic member and the other end is movably carried in a guide rail channel. The guide rail channel is attached adjacent the support pedestal and has a pre-selected curved shape which assures that the movable end of the elastic member is always positioned such that the elastic member freely takes on the shape of any one of a family of parabolictype curves when'the support arm is selectively positioned.

In an alternative embodiment, an arcuate support arm is utilized to control the movement of the movable end of the elastic member. The arcuate support arm is positioned opposite the supportt pedestal with one end attached to a base member and one end attached to a vertical support member, the base member and support members being generally perpendicular to one another. A positioning member attached to the movable end of 0 the elastic member is slideably positioned in a support block which is carried along a channel in the arcuate support arm. A positioning knob allows the support block to be locked in a selected position on the arcuate support arm thereby fixedly positioning the elastic member in a particular position for drawing one of a family of parabolic-type curves.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a front plan view of one preferred embodiment of the invention;

FIG. 2 is a side elevational view of the apparatus shown in FIG. 1;

FIG. 3 is a detailed perspective view of the guide apparatus for controlling the position of the elastic member of the embodiment shown in FIG. 1;

FIG. 4 is a front plan view of an alternative embodiment of the present invention;

FIG. 5 is a right side elevational view of the embodiment shown in FIG. 4;

FIG. 6 is a left side elevational view of the embodiment in FIG. 4;

FIG. 7 is a detailed sectional view of the locking mechanism taken along the line 7-7 in FIG. 4;

FIG. 8 is a detailed sectional view of the locking mechanism taken along line 8-8 in FIG. 4;

FIG. 9 is a graph showing construction of the specified curve; and

FIG. 10 is a graph showing construction of the guide curve.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring to FIGS. 1-3, wherein like numerals refer to like structural elements, a first preferred embodiment of the present invention incorporates a curvedrawing device 1 comprised of an elastic member 2 having a base end attached to a base member 3 and a movable end attached to the top end 16 of a support arm 4. A bottom end 17 of support arm 4 is attached to the base member 3 by means 'of pivot apparatus 5 which forces the top end to move along an arcuate path. The form of the arcuate path is dictated by the controlled movement of one end of the support arm 4 in an arcuate guide channel 39 which forms part of guide apparatus 6. An alternative preferred embodiment of the present invention is shown in FIGS. 4-8. In the second preferred embodiment, the curved drawing apparatus 51 consists of an elastic member 52 having one end attached to a support pedestal 53 and a mov able end positioned within an arcuate support arm 55 by means of a movable support block 56. An arcuate guide member 54 controls the position of the moving end of the elastic member 52 and the support block 56 allows the elastic member 52 to be locked into a selected position for tracing of a curve along the elastic member. The structure and operation of the first and second embodiments will be described in detail separately.

Referring specifically to the first preferred embodiment shown in FIGS. 1-3, elastic member 2 is a generally thin ribbonlike strip fabricated from a flexible resilient material such as steel or plastic. Elastic member 2 has a base end 8 and a movable end 7. The Applicant has found that by controlling the relative positions of the ends of elastic member 2, it will freely take on a shape at least closely approximating one side of a parabolic curve. While in the preferred embodiment, elastic member 2 is manufactured from steel and has a thick ness of 0.020 inches, a length of 10.5 inches and a width of 0.25 inches, other sizes of elastic member 2 and other materials may also be utilized where appropriate. Elastic member 2 is utilized to draw one side of a parabolic type curve. The second side is a mirror image of the first side and is drawn by turning the drawing device 1 over on its opposite side with the vertex of the curve at the same point and tracing the opposite side of the curve.

To suitably control the relative positions of base end 8 and movable end 7, base end 8 is attached to support pedestal 20 and movable end 7 is attached to top end 16 of support arm 4. As is well known in mathematics, at the vertex of the parabola the parabolic curve is tangent to a line which is parallel to the directrix of the parabola. Because of this property of parabolic curves, the base end 8 of the elastic member 2 is mounted in support pedestal 20 such that it is tangent to a reference line 46 which would be parallel to the directrix of the parabola which is drawn using drawing device 1. As is shown in detail in FIG. 2, to hold base end 8 in a position tangent to reference line 46, a narrow slot-like opening 34 is formed between a top anchor block 32 and a bottom anchor block 33 in support pedestal 20. Opening 34 has a generally thin cross section matching the cross section of elastic member 2 and lies generally parallel to horizontal reference line 46. In constructing drawing device 1, the anchored end 8 of elastic member 2 is inserted in opening 34 between attachment means consisting of anchor blocks 32 and 33, and the anchor blocks are then forced together to tightly hold the base end of elastic member 2. The anchor blocks are held in this locking position by tightening screws 35 or similar devices.

Movable end 7 of elastic member 2 is attached to top end 16 of support arm 4 by means of an attachment member 9. As is shown in FIGS. 1 and 2, attachment member 9 consists of opposed side elements 10 which are attached to top end 16 of support arm 4. The bottom edges of side elements 10 are joined together by means of a base element 11. Elastic member 2 is attached to attachment member 9 by means of opposed openings, each designated by the numeral 12, in each of side elements 10. A pivot pin 14 extends through pin openings 12 and through a pivot sleeve 13 attached to the end of elastic member 2. This mechanism allows the end of elastic member 2 to freely pivot while it is being guided by the movement of support arm 4. This pivoting movement of the end of elastic member 2 allows it to freely take on the shape of an exponential type curve.

To properly control the relative positions between the two ends (7 and 8) of elastic member 2, the bottom portion of support arm 4 is mounted on support pedestal such that it can pivot and slide. To accomplish this, pivot apparatus 5 is provided. As is shown in detail in FIG. 3, pivot apparatus 5 comprises a support arm guide which is attached to the top portion of support pedestal 20 by means of a hinge 29 having opposed hinge plates, each designated by the numeral 30 interconnected by a hinge pin 31. Support arm 4 is slidably mounted in an opening 27 which is formed between opposed side elements 26 which form a part of support arm guide 25. Slide opening 27 has generally the same cross section as the cross section of support arm 4 so that lateral movement of support arm 4 in slide opening 27 is restricted. Pivot apparatus 5 allows support arm 4 to move in an are which lies in the same plane as elastic member 2.

Having described those portions of drawing device 1 which allow elastic member 2 to be positioned with base end 8 tangent to a coordinate system reference line and movable end 7 movable in an arcuate manner, the detailed description of the remaining apparatus would be better understood in light of the following description of the geometry which dictates the structure of drawing device 1. As is shown in FIG. 9, when a single parabola (e.g. curve 100, 101 or 102) is drawn, any one segment of the curve is partially described by the arcuate length L (e.g. L1, L2, or L3) measured along the parabola between the vertex and a selected point on the parabola, and by a straight line distance D (e.g. D1, D2 or D3) which is measured between the vertex and the selected point on the parabola. L and D can be measured for any one parabolic curve. In FIG. 9, three parabolic curves 100, 101 and 102 are drawn having a common vertex, V. Each of these curves would have the same geometrical equation of the general form X (K/y )y, with a different value of K for each curve. Thus, three parabolas of a family of parabolas are shown in FIG. 9, each having a K value of K1, K2 and K3. If a point is selected on each of the parabolic curves in FIG. 9 with equal arcuate distance from the vertex, i.e. lengths L1, L2, and L3 are identical, a curve can be drawn through these selected points as is shown in FIG. 9. This curve will be termed the specified curve. The straight line distance between the vertex and the selected points on the specified curve, i.e. D1, D2 and d3, each have different lengths. The Applicant has found that if a flexible resilient elastic member is positioned with one end tangent to a line parallel to the directrix at the vertex and a second end lying on the specified curve, the elastic member will freely take on a shape at least closely approximating a parabola between these two points.

To assure that one end of the elastic member is positioned on the specified curve, the Applicant has utilized his drawing device 1 to control the distance D between the vertex V and the movable end of the elastic member. In particular, since the distance D is always less than the arcuate length L, if a rigid arm (e.g. support arm 4) equal to or larger than the measured arcuate length L has one end attached to the movable end of the elastic member, and if the rigid arm is allowed to rotate and slide through the vertex of the family of parabolas as the movable end of the elastic member is moved along the specified curve, then a second curve is traced in the quadrant of the coordinate system diametrically opposite the quadrant in which the specified curve lies. This generated curve is known as the guide curve and is shown schematically in FIG. 10. Wherein a line of constant length LL has been rotated through vertex V with one end on the specified curve to generate the guide curve. The Applicant has utilized this theory in designing drawing device 1 with arm 4 and guide apparatus 6 which assure that movable end 7 should be noted that in thepreferred embodiment, thesupport arm 4 does not rotate about the vertex of the parabola formed by elastic member 2. However, the positioning of the point of rotation of support arm 4 need not coincide with vertex V as long as the guide curve is designed to compensate for the shifting of the center of rotation from the vertex to an alternative location. In the preferred embodiment, this alternative pivot location is the position of hinge pin 31. The guide curve can be determined mechanically by drawing a family of parabolas, and laying out a specified curve.

An elongated member is then pivoted and moved through the selected pivot point with the top end of the elongated member always resting on the specified curve. The base end of the elongated member then traces the guide curve which will be utilized to construct a curve drawing device 1 which utilizes the shifted pivot point.

Referring to FIGS. 1-3, bottom end 17 of support arm 4 is fixed in the guide channel 39 which is formed between opposed guide rails, each designated by the numeral 37. A guide means comprising a guide roller 18 attached to the end of support arm 4 has an annular indentation which rides on the opposed guide rail edges, each designated by the numeral 38. In the preferred embodiment, guide apparatus 6 comprises two opposed guide rail members, each designated by the numeral 36. By utilizing opposed guide track or rail members 36, support arm 4 is positioned between the guide rail members such that a guide roller 18, positioned on each side of support arm 4, is mounted in a separate, but identical guide channel 39.

The guide curve which is formed by the guide edges 38 has the particular shape describedearlier which assures that movable end 7 of elastic member 2 follows the specified curve. As was noted earlier, guide curve 38 may be generated by pivoting support arm 4 about hinge pin 31 and moving the movable end of elastic member 2 along a specified curve while at the same time making a tracing of the arcuate movement of the bottom end of support arm 4. This tracing of the arcuate movement of support arm 4 would then serve as the guide curve formed between the opposed guide edges 38. Different guide curves will be formed for different types of parabolic curves and for curves having different lengths. For very long parabolic type curves, the elastic member 2 would have an extended length and for very short parabolic type curves the elastic member 2 would be constructed in a shorter length. The present invention does not depend upon the overall size of the curve-drawing device I but rather on the manner in which the elastic member 2 is mounted utilizing support arm 4.

An alternative embodiment 51 of the present invention is shown in FIGS. 48. The principle of operation is generally the same as with the first preferred embodiment. However, elastic member 52 has a movable end 58 which is controlled by means of an arcuate guide arm 54. An arcuate support arm 55 fixedly positions movable end 58 as will be described in detail later.

Curve-drawing device 51 utilizes a positioning member 60 which is an extension of elastic member 52.,Positioning member 60 is a rectangular bar integrally at tached to movable end 58-. of elastic member 52. Each of these elements is co'nst'ru'cted'to form a device 51 6 which can be positioned and operated on either side to allow-each of two sides of a parabolic type curve to be drawn by turning device 51 to the opposite side.

To control the'position of movable end 58 of elastic member 52,-arcuate guidearm 54 is comprised of opposed guide rails, each designated by the numeral 63, which enclose a guide channel 65. A guide pin 61 attached to positioning member 60 protrudes through guide channel 65. As guide pin 61 moves along guide channel 65, the curved shape of guide channel 65 dictates the movement of movable end 58 of elastic member 52. As was the case in drawing device 1 described earlier, by controlling the movement of movable end 58 of elastic member 52, elastic member 52 will freely take on the general shape of a parabolic-type curve. In the case of drawing device 51, guide channel 65 is formed by the curved shape of opposed guide rail edges, each designated by the numeral 64. The curved shape of guide channel 65 is the specified curve referred to in the earlier description of drawing device 1. In this embodiment, the specified curve is formed from apparatus positioned in the same quadrant as is the elastic member 52. The specified curve which forms guide channel 65 is dictated by the same geometry which was described in detail earlier. In the construction of drawing device 51, the specified curve may be generated in the same manner as was described earlier by utilizing a family of parabolic curves.

In addition to restraining the arcuate movement of movable end 58 of elastic member 52, the Applicant has found that it is also necessary to control the angular position of movable end 58 in this preferred embodiment. In particular, the Applicant has found that it is necessary that the movable end 58 of elastic member 52 always be perpendicular to a particular curve. The particular curve can be described as follows. A line is drawn tangent to each of the family of parabolas at the point where the individual parabolas intersect the specified curve. For a detailed description of the specified curve, see the earlier description in this patent specification. Next, an arbitrary distance is laid off on the tangent lines from the point of tangency. This distance is laid off on each of the tangent lines. A second line is then drawn through each of the tangent lines at the laid off distant point, this second line being perpendicular to the tangent line. The array of secondary lines which are formed in this manner will intersect one another at various points. The locus of all of these points of intersection forms what will be termed as X curve. By positioning the movable end 58 of elastic member 52 such that it is always perpendicular to this X curve, the Applicant has found that the elastic member 52 is suitably positioned so that a parabolic-type curve can be traced along it. To assure that the movable end 58 is in fact always perpendicular to the X curve, drawing device 51 utilizes a support block 56 which is restrained by means of a support rail channel 69 which is formed in the support arm 55. In this embodiment, support block or member 56 rides along support rail channel 69 by means of a roller equiped positioning pin 70 which is attached to support block 56 and which extends through channel 69. A second roller equiped pin 70a is also attached to support block 56 and also extends through channel 69. A positioning knob or locking means 71 isthreadably attached to the second positioning pin 70a and can be threadably tightened against support rail 68. This tightening of positioning knob 71 allows the support block 56 to be locked into a fixed position which secures the position of elastic member 52. Since support block 56 is maintained in position in channel 69 by a two point apparatus, i.e. positioning pins 70 and 70a, an opening 57 in support block 56 through which positioning member 60 is slidably inserted, will always position the movable end 58 of elastic member 52 in a proper position perpendicular to the X curve formed by support arm 55. As is shown in detail in FIG. 7, opening 57 has generally the same cross-sectional shape as positioning member 60. This restricts the lateral movement of positioning member 60 relative to support block 56 and assures the proper perpendicular position of movable end 58 of elastic member 52 relative to channel 69. As is shown in F IG. 4, guide channel 69 is formed from opposed support rails, each designated by the numeral 68, which are a part of support arm 55. Support rails 68 are generally thin, curved members.

As in the case of curve-drawing device 1, base end 59 of elastic member 52 is held in a support pedestal 53 with elastic member 52 tangent to a horizontal reference line 78. Thiis is accomplished by securing the generally rectangular base end 59 in an attachment means comprising a matching rectangular opening 76 in support pedestal 53. Drawing device 51 utilizes a base member 74 and a vertical support member 75 to which are attached the ends of arcuate support arm 55 and the ends of guide arm 54. Each of members 74 and 75 is a generally rectangular bar-like member. The top end 67 of guide arm 54 is screwed or otherwise attached to the top end of vertical support member 75. The bottom end of guide arm 54 expands into a bottom support member 66 which is screwed or otherwise attached to base member 74. Similarly, the top end 73 of support rail 68 is attached to the top of vertical support member 75 generally adjacent the end of guide arm 54 and the bottom end 72 is screwed or otherwise attached to base member 74. Vertical support member 75 and base member 74 are generally perpendicular to one another with the support pedestal 53 attached to each of the members generally at their intersection point. One of the major advantages of drawing device 51 is that by loosening and tightening positioning knob 71, elastic member 52 is held in a fixed position such that a curve can be more easily drawn along it or a duplicate parabolic curve can be drawn on any one of a number of coordinate systems by simply moving the drawing device 51 from one coordinate system to another. By reversing device 51 and laying it on its back side, the second side of the parabolic type curve can be drawn. To accomplish this, members 700 and 71 are removable from one side and insertable in the opposed side by threaded attachment or similar means (not shown).

The operation of drawing device 1 and device 51 can be summarized as follows. Generally, an exponential or parabolic-type curve will be drawn on an existing coordinate system having a horizontal axis and a vertical axis. Typically, in plotting scientific data it is desirable that the exponential or parabolic type curve be drawn through a particular data point on the coordinatesystern. Thus, either drawing device 1 or drawing device 51 is laid flat on top of the coordinate system with the horizontal refrence line positioned parallel to the horizontal reference line on the coordinate system. The intersection of the vertical and horizontal reference lines is positioned where it is desired that the vertex of the drawn parabola be. The support arm 4 is then moved until elastic member 2 lies on the reference data points. A curve is then drawn along elastic member 2. In the case of drawing device 51, the positioning knob 71 may be tightened down when the elastic member 52 is positioned on the reference data point. Elastic member 52 is then held in a fixed position for drawing the curve or for drawing similar curves as the drawing device is moved. The opposite side of the parabola is drawn by turning over device 51 after moving pin a to the opposite side of device 51.

As was pointed out earlier, by properly restraining a resilient elastic member the Applicant has found that a parabolic-like curve is formed by the member. The Applicant realizes that the proximity of the curve to a parabola varies somewhat. However, for most drafting purposes, the curve which is traced using Applicants invention is sufficiently like a true parabola to form a parabolic type curve. In addition, the present invention can be built in various sizes and can be utilized for drawing various exponential curves.

What is claimed is:

1. Apparatus for use in drawing exponential type curves on a coordinate system, comprising:

a. a base member selectively positionable on the coordinate system;

b. a thin, elongated elastic tracing member having a base end and a movable end, said elastic member generally assuming a planar exponential curve shape along which one side of a parabolic like curve can be drawn when said ends are selectively positioned;

c. attachment means for attaching the base end of said elastic member to said base member such that the base end of said curved elastic member remains generally tangent to a selected line in the coordinate system as the position of said movable end is varied;

d. a support arm for guiding said elastic member and having first and second ends, said second end pivotally connected to the movable end of said elastic member;

e. support arm connecting means for pivotally and slideably connecting said support arm to said base member;

f. a guide track attached to said base member, said guide track having a pre-selected planar curved shape, in which the first end of said support arm is guided by said track to control the positioning of the first end of said support arm, said curve being generally coplanar with said flexible strip;

g. guide means for operably connecting said support arm first end to said guide track to control the positioning of said support arm; whereby movement of said first end of said support arm along said track will cause movement of said second end of said support arm along with sliding and pivoting meovement of said support arm with respect to said base by said support arm connecting means such that the movable end of said tracing member will be moved to cause said tracing member to assum a different curved shape.

2. The drawing apparatus of claim 1 wherein said support arm connecting means include:

a. a guide element having an opening for receiving said support arm therein, said support arm slideable axially within said opening as said support arm first end moves along said guide track; and

9 b. a pivot element attached to said guide element and to said base member to allow said guide element and support arm to rotate in a plane generally parallel to the plane in which the exponential curve is being drawn.

3. The drawing apparatus of claim 2 wherein said elastic member is a thin ribbon-like strip.

4. The drawing apparatus of claim 2 wherein said guide means include a roller member rotatably attached to said fupport arm first end, the peripheral edge of said roller member being engagable with said guide track to maintain said support arm first end adjacent thereto.

5. Apparatus for use in drawing exponential type curves on a coordinate system, comprising:

a. an elongated base member;

b. an elongated vertical member having one end attached to one end of said base member, said vertical and base members being generally coplanar;

c. a thin, elongated elastic tracing member having a base end and a movable end, said elastic member generally assuming a planar exponential curve shape along which one side of a parabolic like curve can be drawn when said ends are selectively positioned;

d. attachment means for attaching the base end of said elastic member to said base member such that said elastic member base end remains generally tangent to a selected line in the coordinate system as the position of said movable end is varied;

e. an arcuate support arm for controlling said elastic member and having first and second ends, one of said ends attached to said base member and one of 10 said ends attached to said vertical member said arcuate support arm containing a channel-like opening; a support member slidable along said channel-like opening and slideably receiving the movable end of said elastic member therein and movable along said support arm channel to maintain the movable end of said elastic member in a position generally perpendicular to a tangent drawn to the pre-selected curved shape of said support arm channel; an arcuate guide track having first and second ends with one end attached to said base member and one end attached to said vertical member such that the distance between said support arm and said arcuate guide track at the point at which they attach to said vertical member is different from the distance between them at the point where they attach to said base member, and guide track generally lying in a plane parallel to the plane of said flexible strip; guide pin means attached to said tracing member and being slideable in said arcuate track; whereby movement of said support member along said arcuate support arm will cause said guide pin means to move along said arcuate guide track and the movable end of said tracing member will slide with respect to said support member thus causing said tracing member to assume a different curve. 6. The drawing apparatus of claim 5 including locking means for selectively positioning said support member relative to said support arm channel to fixedly position the elastic member to allow a curve to be traced along it.

TJNTTED STATES PATENT OFFICE CERTH ECATE 0F CORRECTION PATENT NO. 3,927,477 a QATED Dec. 23, 1975 Page 1 of 2 mvmrorus) Timothy L. Harris it is certified that error appears in the above-identified patent and that said Letters Patent Q are hereby corrected as shown below:

Column 2, Line 4 "supportt" should be support-- Column 2, Line 30 "ment in" should be --n \ent shown in Column 4, Lines 38 and 3 9 specified curve should have quotes Qaround it specified curve"- Colman 4, Lines 62 and 63 guide curve should have quotes around it =-=-"guide curve"- Column 4 Line 65 specified curve should have quotes around it specified curve"-- Column 4, Line 66' guide curve should have quotes around it -"guide curve"-- Q 7 Column 6 Line 19 -'specified curve should have quotes around it =--"specified curve" Column 6, Line 49 "as" should be --an--' Column 6, Line 51 X should have quotes around it --"X"-- Column 6, Line 55 X should have quotes around it -"X"-- Column 7,, Line 8 X should have quotes around it -"X"-- Column. '7, Line 22 "Thiis" should be --This-- UNITED STATES PATENT OFFICE CERTIFICATE OF CORECTIN Q PATENT NO. 2 3,927 477 DATED Dec. 23, 1975 Page 2 of 2 mvrzrrrorrts) Timothy L. Harris It is certified that error appears in the above-identified patent and that said Letters Patent Q are hereby corrected as shown below:

. Column 8 Line 55 after "ment of" insert said guide means and-- Column 8, Line 58 "me ovement" should be -movemnt-- Column 9, Line 10 "fupport" should be- --support- Column 10, Line 18 "and" should be said-- Signed stated this 9 fourth Day of May 1976 [SEAL] Arrest:

Q RUTH C. MASON C. MARSHALL DANN Arresting Officer (mnmissr'mrvr uj'lurrints and Trademark-x 

1. Apparatus for use in drawing exponential type curves on a coordinate system, comprising: a. a base member selectively positionable on the coordinate system; b. a thin, elongated elastic tracing member having a base end and a movable end, said elastic member generally assuming a planar exponential curve shape along which one side of a parabolic like curve can be drawn when said ends are selectively positioned; c. attachment means for attaching the base end of said elastic member to said base member such that the base end of said curved elastic member remains generally tangent to a selected line in the coordinate system as the position of said movable end is varied; d. a support arm for guiding said elastic member and having first and second ends, said second end pivotally connected to the movable end of said elastic member; e. support arm connecting means for pivotally and slideably Connecting said support arm to said base member; f. a guide track attached to said base member, said guide track having a pre-selected planar curved shape, in which the first end of said support arm is guided by said track to control the positioning of the first end of said support arm, said curve being generally coplanar with said flexible strip; g. guide means for operably connecting said support arm first end to said guide track to control the positioning of said support arm; whereby movement of said first end of said support arm along said track will cause movement of said second end of said support arm along with sliding and pivoting meovement of said support arm with respect to said base by said support arm connecting means such that the movable end of said tracing member will be moved to cause said tracing member to assume a different curved shape.
 2. The drawing apparatus of claim 1 wherein said support arm connecting means include: a. a guide element having an opening for receiving said support arm therein, said support arm slideable axially within said opening as said support arm first end moves along said guide track; and b. a pivot element attached to said guide element and to said base member to allow said guide element and support arm to rotate in a plane generally parallel to the plane in which the exponential curve is being drawn.
 3. The drawing apparatus of claim 2 wherein said elastic member is a thin ribbon-like strip.
 4. The drawing apparatus of claim 2 wherein said guide means include a roller member rotatably attached to said fupport arm first end, the peripheral edge of said roller member being engagable with said guide track to maintain said support arm first end adjacent thereto.
 5. Apparatus for use in drawing exponential type curves on a coordinate system, comprising: a. an elongated base member; b. an elongated vertical member having one end attached to one end of said base member, said vertical and base members being generally coplanar; c. a thin, elongated elastic tracing member having a base end and a movable end, said elastic member generally assuming a planar exponential curve shape along which one side of a parabolic like curve can be drawn when said ends are selectively positioned; d. attachment means for attaching the base end of said elastic member to said base member such that said elastic member base end remains generally tangent to a selected line in the coordinate system as the position of said movable end is varied; e. an arcuate support arm for controlling said elastic member and having first and second ends, one of said ends attached to said base member and one of said ends attached to said vertical member said arcuate support arm containing a channel-like opening; f. a support member slidable along said channel-like opening and slideably receiving the movable end of said elastic member therein and movable along said support arm channel to maintain the movable end of said elastic member in a position generally perpendicular to a tangent drawn to the pre-selected curved shape of said support arm channel; g. an arcuate guide track having first and second ends with one end attached to said base member and one end attached to said vertical member such that the distance between said support arm and said arcuate guide track at the point at which they attach to said vertical member is different from the distance between them at the point where they attach to said base member, and guide track generally lying in a plane parallel to the plane of said flexible strip; guide pin means attached to said tracing member and being slideable in said arcuate track; whereby movement of said support member along said arcuate support arm will cause said guide pin means to move along said arcuate guide track and the movable end of said tracing member will slide with respect to said support member thus causing said tracing member to assume a different curve.
 6. The drawing apparatus of claim 5 including locking means for selectively positioning said support member relative to said support arm channel to fixedly position the elastic member to allow a curve to be traced along it. 